<p dir="ltr">Network models are essential for representing a myriad of real-world problems. Two of the most important categories of networks are centralized and distributed networks. In this thesis, we investigate the efficient resource allocation for one centralized communication network and two distributed epidemic networks.</p><p dir="ltr">In Chapter 2, we study three proposed centralized coded caching schemes with uncoded pre-fetching for scenarios where end users are grouped into classes with different file demand sets. We provide a lower bound for the transmission rate for the system with heterogeneous user profiles. Then the transmission rates of the three schemes are compared with the lower bound to evaluate their gap to optimality, and also compared with each other to show that each scheme can outperform the other two when certain conditions are met. Finally, we propose a cache distribution method that results in a minimal peak rate and a minimal average rate for one of the schemes when the users’ storage is relatively small compared with the size of the library.</p><p dir="ltr">In Chapter 3, we examine a discrete-time networked SIR (susceptible-infected-recovered) epidemic model, where the infection, graph, and recovery parameters may be time-varying. We propose a stochastic framework to estimate the system states from observed testing data and provide an analytic expression for the error of the estimation algorithm. We validate some of our assumptions for the stochastic framework with real COVID-19 testing data. We identify the system parameters with the system states from our estimation algorithm. Employing the estimated system states, we provide a novel distributed eradication strategy that guarantees at least exponential convergence to the set of healthy states. We illustrate the results via simulations over northern Indiana, USA.</p><p dir="ltr">In Chapter 4, we propose a novel discrete-time multi-virus SIR model that captures the spread of competing SIR epidemics over a population network. First, we provide a sufficient condition for the infection level of all the viruses over the networked model to converge to zero in exponential time. Second, we propose an observation model which captures the summation of all the viruses’ infection levels in each node, which represents the individuals who are infected by different viruses but share similar symptoms. We present a sufficient condition for the model to be strongly locally observable. We propose a distributed Luenberger observer for the system state estimation. We demonstrate how to calculate the observer gain for the estimator and prove that the estimation error of our proposed estimator converges to zero asymptotically with the observer gain found. We also propose a distributed feedback controller which guarantees that all viruses are eradicated at an exponential rate. We then show via simulations that the estimation error of the Luenberger observer converges to zero before the viruses die out.</p><p dir="ltr">We conclude in Chapter 5, where we summarize the findings of this thesis and introduce several challenging open research questions that arise from its results. These questions encompass a range of topics, including the design of optimal testing strategies for large populations, the investigation of estimation techniques in the presence of noisy measurement models, the extension of the SIR epidemic model to more complex models like SEIR and SAIR, and the exploration of efficient vaccine allocation schemes.</p>

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The demands of a modern way of life have changed the way power electronics systems work. For instance, the grid has to provide not only the service of delivering electrical energy but also the communication to enable interactions between customers and enable them to be producers of electrical energy, too. Thus, the smart grid has come into existence. The consequence of the smart grid is that consumers could be “smart.” The most obvious consumers are households, so the houses have to also be smart and must be equipped with various power electronics devices for producing and managing electrical energy. Again, all those devices have to communicate somehow and provide data for managing electrical energy in the house. Zoomed in further, novel, state-of-the-art measurement equipment could have been built from different power electronics devices, and communication among them would be necessary for good operation. Zoomed further in, communication among different pieces of power electronics devices (such as converters) could offer benefits such as flexibility, abstraction, and modularity. This thesis provides insight into different communication techniques and protocols used in power electronics systems. A top-down approach presents three different levels of communication used in real-life projects with all the challenges they bring, starting with the smart house, followed by the state-of-the-art impedance measurement unit, and finalizing with internal power electronics building block (PEBB) communication. In the case of a smart house, where the house is equipped with solar panels, charge controllers, batteries, and inverters, communication allows interoperation between different elements of the power electronics system, enabling energy management. Results show the operation of the system and energy management algorithm. A house of this type won first prize at an international competition where energy management was one of the disciplines. The impedance measurement unit consists of different power electronics devices. In this case, too, communication between devices enables the operation of the impedance measurement unit. Communication techniques used here are shown together with measurement results. Finally, inter-PEBB communication has been shown as an approach for interaction among the different elements inside the PEBB, such as controller, GDs, sensors, and actuators. Real-time communication protocol, including all challenges, is described and developed. This approach is shown to enable communication and synchronization among different nodes inside the PEBB. Communication enables all internal elements of the PEBB to be transparent outside the PEBB in the sense that data gathered from them could be reused anywhere else in the system. Also, this approach enables the development of distributed event (time) driven control, hardware and software, abstraction, high modularity, and flexibility. A very important aspect of inter-PEBB communication is synchronization. A simple technique of sharing a clock among the parts of a 6 kV PEBB has been shown. / M.S. / This thesis provides insight into different communication techniques and protocols used in power electronics systems. A top-down approach presents three different levels of communication used in real-life projects with all the challenges they bring, starting with the smart house and a custom device designed and developed to be a communication interface among different power electronics devices from different vendors, such as charge controllers or inverters, but with capabilities not only to communicate but to also provide a platform for the development of energy management algorithms used to make houses grid zero if not grid positive. Aside from the smart house, this thesis describes communication protocols and techniques used in the impedance measurement unit (IMU). This complex measurement device provides valuable and accurate impedance measurements and consists of different power electronics devices that need to communicate. Finally, at the power electronics building block (PEBB) level, real-time communication protocol with all challenges is described. Developed communication protocol provides communication and synchronization among different nodes such as GDs, sensors, and actuators inside the PEBB. This intra-PEBB communication and synchronization combined with inter-PEBB communication and synchronization provide the foundation for the development of truly distributed event- (time-) driven control as well as hardware and software abstraction.

Les exigences croissantes sur l'efficacité énergétique des bâtiments, l'évolution du {marché} énergétique, le développement technique récent ainsi que les particularités du poste de chauffage ont fait du MPC le meilleur candidat pour la régulation thermique des bâtiments à occupation intermittente. Cette thèse présente une méthodologie basée sur la commande prédictive distribuée visant un compromis entre l'optimalité, la simplicité et la flexibilité de l'implantation de la solution proposée. Le développement de l'approche est progressif : à partir du cas d'une seule zone, la démarche est ensuite étendue au cas multizone et / ou multisource, avec la prise en compte des couplages thermiques entre les zones adjacentes. Après une formulation quadratique du critère MPC pour mieux satisfaire les objectifs économiques du contrôle, la formulation linéaire est retenue. Pour répartir la charge de calcul, des méthodes de décomposition linéaire (comme Dantzig-Wolfe et Benders) sont employées. L'efficacité des algorithmes distribués proposés est illustrée par diverses simulations. / The increasing requirements on energy efficiency of buildings, the evolution of the energy market, the technical developments and the characteristics of the heating systems made of MPC the best candidate for thermal control of intermittently occupied buildings. This thesis presents a methodology based on distributed model predictive control, aiming a compromise between optimality, on the one hand, and simplicity and flexibility of the implementation of the proposed solution, on the other hand. The development of the approach is gradually. The mono-zone case is initially considered, then the basic ideas of the solution are extended to the multi-zone and / or multi-source case, including the thermal coupling between adjacent zones. Firstly we consider the quadratic formulation of the MPC cost function, then we pass towards a linear criterion, in order to better satisfy the economic control objectives. Thus, linear decomposition methods (such as Dantzig-Wolfe and Benders) represent the mathematical tools used to distribute the computational charge among the local controllers. The efficiency of the distributed algorithms is illustrated by simulations.

Le développement simultané de terminaux mobiles multimédia (smartphones, tablettes) et de réseaux d’accès offrant des débits élevés conduit à une explosion du trafic liés aux contenus multimédia. Cette croissance nécessite un partage efficace des ressources radio entre fournisseurs de contenus (dans le cas de la diffusion) ou entre récepteurs (dans le cas de services de vidéo à la demande). Cette thèse propose des outils de partage équitable des ressources en termes de qualité des contenus multimédia reçu et de délai de transmission dans les deux contextes précédents. La variété des compromis débit-distorsion des contenus multimédia est exploitée à cet effet. Dans un premier temps, une solution centralisée de contrôle conjoint du débit de codage et de transmission de plusieurs programmes transmis sur un même canal est considérée. L’objectif est de fournir des flux de qualités similaires avec des variations limitées, tout en assurant des délais de transmission comparables. Ce problème est résolu en synthétisant une commande prédictive à l’aide d’outils d’optimisation sous contrainte. Dans un second temps, seule l’allocation de bande est centralisée, le contrôle des caractéristiques de compression de chaque flux est réalisé de manière distribuée. Le contrôleur centralisé ne renvoie que le niveau de remplissage des tampons associés à chaque flux aux fournisseurs de contenus distants. Une stratégie de régulation des débits de codage est alors mise en place par ces fournisseurs, de manière à réguler le niveau en bits ou en image des tampons. La stabilité de ce système de régulation couplé est étudiée en détails. Enfin, l’optimisation inter-couches d’une chaine de transmission de contenus multimédia scalable est considérée. Ce problème est formulé dans le contexte de la programmation dynamique. Lorsque des modèles de complexité raisonnable sont considérés et avec des caractéristiques du système bien connues, des solutions optimales peuvent être obtenues. Des techniques d’apprentissage sont mises en œuvre, lorsque le système n’est que partiellement connu, par exemple, lorsque l’état du canal de transmission parvient avec du retard à l’organe de commande. / Due to the emergence of new generation mobiles and media streaming services, data traffic on mobile networks is continuously exploding. Despite the emergence of standards such as LTE, resources still remain scarce and limited. Thus, efficiently sharing resources among broadcasters or between unicast receivers connected to the same base station is necessary. An efficient resources allocation, where a fair received video quality between users and an equal transmission delay are achieved, is targeted. To that end, the variety of the rate-distortion trade-off of multimedia content is exploited. First, a centralized joint encoding and transmission rate control of multiple programs sharing the same channel is considered. A satisfactory and a comparable video quality among the transmitted programs, with limited variations, as well as a comparable transmission delay are targeted. The problem is solved using constrained optimization tools. Second, only the bandwidth allocation control is centralized, the control of the encoding rate characteristics of each stream is carried in a distributed manner. By modeling the problem as a feedback control system, the centralized bandwidth allocation is required to feed back only the buffer level to its associated remote content provider. The equilibrium and stability issues are addressed for both bit and second buffer control. In the case of simple unicast connection, a cross-layer optimization of scalable video delivery over wireless channel is performed. The optimization problem is cast in the context of dynamic programming. When low complex model are considered and when the system characteristics are known, optimal solutions can be obtained. When the system is partially known, for example, when the state of the channel reaches the control process with delay, learning techniques are implemented.

L’incorporation des instruments intelligents dans les boucles de sécurité nous mène vers une sécurité intelligente et les systèmes deviennent des « systèmes instrumentés de sécurité à intelligence distribuée (SISID) ». La justification de l’usage de ces instruments dans les applications de sécurité n’est pas complètement avérée. L’évaluation de la sûreté de fonctionnement de ce type de systèmes n’est pas triviale. Dans ce travail, la modélisation et l'évaluation des performances relatives à la sûreté de fonctionnement des systèmes instrumentés de sécurité (SIS) sont traitées pour des structures intégrant de l’intelligence dans les instruments de terrain. La méthodologie que nous utilisons consiste en la modélisation de l’aspect fonctionnel et dysfonctionnel de ces systèmes en adoptant le formalisme basé sur les réseaux de Petri stochastiques qui assurent la représentation du comportement dynamique de ce type de systèmes. La modélisation est traitée sous la forme d’une approche stochastique utilisant les réseaux d’activité stochastiques SAN (Stochastic Activity Network). L’introduction d’indicateurs de performances permet de mettre en évidence l’effet de l’intégration des niveaux d’intelligence dans les applications de sécurité. La méthode de Monte Carlo est utilisée pour évaluer les paramètres de sûreté de fonctionnement des SIS en conformité avec les normes de sécurité relatives aux systèmes instrumentés de sécurité (CEI 61508 et CEI 61511). Nous avons proposé une méthode et les outils associés pour approcher cette évaluation par simulation et ainsi apporter une aide à la conception des systèmes instrumentés de sécurité (SIS) intégrant quelques fonctionnalités des instruments intelligents / The incorporation of intelligent instruments in safety loops leads towards the concept of intelligent safety and the systems become “Intelligent Distributed Safety Instrumented Systems (IDSIS)”. The justification for using these instruments in safety applications is not fully proven and the dependability evaluation of such systems is a difficult task. Achieved work in this thesis deals with modelling and thus the performance evaluation relating to the dependability for structures which have intelligence in the instruments constituting the Safety Instrumented Systems (SIS). In the modelling of the system, the functional and dysfunctional aspects coexist and the dynamic approach using the Stochastic Activity Network (SAN) is proposed to overcome the difficulties mentioned above. The introduction of performance indicators highlight the effect of the integration of intelligence levels in safety applications. Monte-Carlo method is used to assess the dependability parameters in compliance with safety standards related to SIS (IEC 61508 & IEC 61511). We have proposed a method and associated tools to approach this evaluation by simulation and thus provide assistance in designing Safety Instrumented Systems (SIS) integrating some features of intelligent tools